Won my first online fight by mashing buttons (I still haven't played lesson mode). I'm terrible at fighters. :3
Also, the trophy list appears to be global (shared with N. America and Japan). It's also named "Persona 4 ARENA Trophy", which annoys me to no end.
The game seems to be really good, but I'll put Story mode on hold until I finish my second playthrough of Persona 4 Golden (need to see Margaret's NG+ content for the first time).
Interesting that the trophy list is global; Atlus games normally have a separate trophy list per region.
As far as them having the "Trophy" bit at the end, I think most Atlus games do that. And yeah, it's super annoying.